MODELING OF DYNAMIC PROPERTIES OF THECOMPOSITE SHELL FOR TV TOWER

Miroslav J. CernyCzech Technical University in Prague, Klokner Institute

Solinova 7, 16608 Prague 6cerny@klok.cvut.cz

SUMMARY

Dynamic properties of composite shell have been investigated experimentally andnumerically. Eigenvalues have been evaluated by impact testing from output signal inthe mesh of points and their frequency spectrum. The eigenvalues have been furthercalculated numerically by QR iteration of the finite element method and compared.

Keywords: composites, modeling, testing ,dynamic properties, finite element method

INTRODUCTION

Fibre composites with polymer matrix have been already used on TV towers andtransmitters. Polymer composites have outstanding dielectric and corrosion propertiesimportant for such an application. As an example have been chosen the composite shellsfor TV towers. Recently, composite shells have been used for cladding at the 3rd floor

Fig.1 TV Tower Praded (1492 m above sea level)

gallery of TV Tower Praděd (1492 m above sea level, Fig.1). The shells of length 4500

mm, width 1684 mm and clearance 400 mm have been supported at top and bottom bysteel structure of gallery, adjacent longitudinal edges have been unsupported. At the 3rdfloor are located radio relay aerials and other equipment. The covering consists of 62composite shells of special sinusoidal shape (Fig.2). Shape of the shells has been

optimized to satisfy requirements for microwave transparency (2- 8 GHz), airflow andsufficient stiffness. The thickness of the shell should correspond to requirements formicrowave permeability. Shells were fabricated from laminated G/UP composite withpolyester isophtalic resin. Two alternatives of reinforcement have been evaluated:woven and unidirectional glass fabrics interlaced by mats.

Fig.2 Assembly of composite shells

MATERIAL PROPERTIES OF THE COMPOSITE

The mechanical properties of the composite have been found out from mechanical tests.Two alternatives of composites have been considered: (1) The composite with thickness9.8 mm consisted of 6 layers of woven glass fabric 500 g.m-2 or (2) 6 layers ofunidirectional glass fabric Rovinap 42-08 interlaced by 10 layers of glass mat 450 g.m-2

and both surfaces laminated by glass mat 300 g.m-2. Polymer resin was isophtalic typeViapal VUP 4686 BET. The following Table 1 shows the obtained test data.

Tab. 1. Material properties

PropertyUnit (1) (2)

Thickness mm 9.8 9.8

Volume weight g.cm-3 1.492 1.521

Glass content % 37.6 41.5

Strength in tension MPa 141 193

E-modulus in tension MPa 17273 25681, 17140

Shear modulus MPa 5976 8870

Poisson’s ratio - 0.24 0.24

DYNAMIC STRUCTURAL ANALYSIS

The aim of dynamic analysis was to evaluate the dynamic properties of the compositeorthotropic and layered shell. The analysis has been focused on first twoeigenfrequencies and eigenmodes of the composite shell. The problem has been solvedby finite element method according to CLT (classic laminate theory) and Lanczos`s

subspace method with tridiagonalisation of matrix B in equation (1) as described byHughes [1]:

( . )B I X− =µ 0 with µω

= 12 (1)

Equation (1) can be obtained from the standard form

by changing the variable

where L is a lower triangular matrix

and assuming

Eigenvalues have been calculated by iteration with QR method. The element used infinite element procedure was DKT (Discrete Kirchhoff Triangle), composite has been

0).( =Φ− MK λ

XL T)( 1−=Φ

TLLK .= (4)

(3)

(2)

TLMLB )( 11 −−= (5)

Fig.3 First eigenmode f1=59.126 Hz Fig.4 Second eigenmode f2=151.97 Hz

modeled from individual layers with orthotropic properties. Analyzed shell has beensimply supported along the curved edges, straight edges were free. Total number ofelements and nodes on symmetrical part of the shell was 396 and 230 respectively.

Following alternatives have been evaluated (see Tab. 2):(1) shell reinforced by woven glass fabric, material orthotropic (E1=E2)(2) shell reinforced by unidirectional glass fabric, material orthotropic (E1>E2), E1 alongthe free edge. Further, two alternatives of boundary conditions along adjacent edgeshave been considered:(a) totaly free edge (case A)(b) lap-joint of adjacent shells with edge cover plate (case B).Some other details of the analysis are described at article of Cerny [2].

Tab. 2. Calculated eigenfrequencies (case A)

Eigenfrequency

[Hz]

E1=E2

(1)

E1>E2

(2)

First 59.126 68.448

Second 151.97 180.530

First and second eigenmode of the shell (E1=E2, free edge, case A) are shown in theFigs.3 and 4 respectively. The calculated eigenfrequencies are shown in Table 2. Theeigenfrequencies for case B are shown in Table 3.

Tab. 3. Calculated eigenfrequencies (case B)

Eigenfrequency

[Hz]

E1=E2

(1)

E1>E2

(2)

First 119.16 134.50

Second 155.31 183.90

DYNAMIC TESTING

Recently, the dynamic properties of structures are measured by a measurement chain,consisting of sensor and measurement unit involving AD (analog- digital) converter. Dynamic measurements of shell structures are mostly realized by accelerometers. The

described procedure has been already used to measure the dynamic properties ofcomposite shell, as shown by Cerny [3].The aim of dynamic testing was to evaluate some dynamic properties of the compositeshell. The work has been focused on eigenvalues of the shell i.e. eigenfrequencies andeigenmodes. The eigenvalues have been evaluated by an impact method. Dynamicresponse on the hammer impact at the top of the shell has been measured at the same

time in two points. The output signal has been measured simultaneously in referenceand current points of the mesh (No.001-513) by 2 accelerometers PCB333, see Fig.5,(Analog Devices, USA) and ADXL05 (Analog Devices, USA) and recorded bymeasurement system Hewlett- Packard 3852. Measured signal was digitised by high-

Fig.5 Mesh of points

speed voltmeter HP 44704A (speed up 100 ksa.s-1) and high-speed multiplexer HP44711A and stored in memory of PC Pentium. The frequency spectrum of signal in 78points has been calculated by FFT analysis in LabWindows package (National

Fig.6 Dynamic measurement at Klokner Institute Facilities

á

Fig.7 Measured signal and frequency spectrum of signal in typical point

Instruments, USA). The results of FFT analysis were used for determination of first twoeigenfrequencies and eigenmodes. Eigenfrequencies have been found from thefrequency spectrum as resonance frequencies. Eigenmodes have been evaluated by themodal analysis from ratio of accelerations in current and reference points on respectiveresonance frequencies.The Fig. 7 shows the frequency spectrum in a typical point obtained by FFT analysiswith three resonance frequencies, corresponding to eigenfrequencies of the compositeshell, Table 4. The resonance frequency 100 Hz corresponds to response of supportingsteel frame, what has been confirmed by a detailed modal analysis.

Tab. 4. Measured eigenfrequencies (case A)

Mode UnitFrequency

1 Hz 53.412 Hz 152.59

CONCLUSIONS

It has been found that the dynamic mechanical behaviour of composite shells is strongdependent on anisotropy of composite material.Results of the analysis and measurement give following eigenfrequencies for case A:first eigenfrequency 59.126 Hz (measured 53.41 Hz) , second eigenfrequency 151.97Hz (measured 152.59). Remarkable are advantageous high damping properties of the

composite shells (see Fig. 7). In case of orthotropy E1>E2 (2) the calculatedeigenfrequencies were 15- 18% higher than for orthotropy E1=E2 (1). Eigenfrequenciesevaluated from test are in a good agreement with the calculation (less than 10%difference).

ACKNOWLEDGEMENTS

This research has been supported by project MSM6840770015.

References

1. Hughes, T.J.R., The Finite Element Method- Linear Static and Dynamic Finite ElementAnalysis. Dover Publishers, New York, 2000.

2. Cerny, M.J., Measurement and Analysis of Dynamic Properties of Composite ShellsSubjected to Wind Loading. Proceedings, 3rd International Conference on Dynamics ofCivil Engineering and Transport Structures and Wind Engineering (DYN-WIND), Boboty,2005.

3. Cerny, M.J., Eigenvalues of Composite Shells for Television Tower Prague. Proceedings,International Conference on Composite Engineering (ICCE/1), New Orleans, 1994